Systems, Methods, and Media for Recording an Image Using an Optical Diffuser

ABSTRACT

Systems, methods, and media for recording an image of a scene are provided. In accordance with some embodiments, systems for recording an image of a scene are provided, comprising: a diffuser that diffuses light representing the scene and that has a scattering function that is independent of aperture coordinates; a sensor that receives diffused light representing the scene and generates data representing an image; and a hardware processor that uses a point spread function to deblur the image.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/522,943, filed Mar. 22, 2013, which is a national stage applicationunder 35 U.S.C. §371 of International Application No. PCT/US2011/022248,filed Jan. 24, 2011, which claims the benefit of U.S. Provisional PatentApplication No. 61/297,667, filed Jan. 22, 2010, each of which is herebyincorporated by reference herein in its entirety.

This invention was made with government support under Grant NumbersN00014-08-1-0329 and N00014-08-1-0638 awarded by the Navy/Office ofNaval Research. The government has certain rights to the invention.

TECHNICAL FIELD

The disclosed subject matter relates to systems, methods, and media forrecording an image using an optical diffuser.

BACKGROUND

For conventional cameras, there is a fundamental trade-off between depthof field (DOF) and noise. Generally, cameras have a single focal plane,and objects that deviate from this plane are blurred due to defocus. Theamount of defocus blur depends on the aperture size and the distancefrom the focal plane. To decrease defocus blur and increase DOF, theaperture size must be decreased, reducing the signal strength of therecorded image as well. In many cases, it is desirable to have a DOFthat is as large as possible so that all details in the scene arepreserved. This is the case, for instance, in machine visionapplications such as object detection and recognition, where it isdesirable that all objects of interest be in focus. However, stoppingdown the lens aperture is not always an option, especially in low lightconditions, because it can increase noise, which in turn can materiallyimpact the recorded image.

SUMMARY

Systems, methods, and media for recording an image of a scene areprovided. In accordance with some embodiments, systems for recording animage of a scene are provided, comprising: a diffuser that diffuseslight representing the scene and that has a scattering function that isindependent of aperture coordinates; a sensor that receives diffusedlight representing the scene and generates data representing an image;and a hardware processor that uses a point spread function to deblur theimage.

In accordance with some embodiments, methods for recording an image of ascene are provided, the methods comprising: diffusing light representingthe scene using a diffuser that has a scattering function that isindependent of aperture coordinates; receiving diffused lightrepresenting the scene and generating data representing an image; andusing a point spread function to deblur the image

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a mechanism for recording an image in accordancewith some embodiments.

FIG. 2 is a combination of two images, one not using a diffuser (a) andone using a diffuser (b), in accordance with some embodiments.

FIG. 3 is a diagram of a lens and a sensor in accordance with someembodiments.

FIG. 4 is a diagram of a lens, a diffuser, and a sensor in accordancewith some embodiments.

FIG. 5 is a diagram illustrating a light field on a sensor in accordancewith some embodiments.

FIG. 6 is a diagram of a ray and the scattering of the ray in accordancewith some embodiments.

FIG. 7 is a combination of point-spread-function andmodulation-transfer-function graph pairs in accordance with someembodiments.

FIG. 8 is a diagram an optical system including a wedge (a) and a randomvarying surface in accordance with some embodiments.

FIG. 9 is combination of diagrams of a diffuser profile (a), a diffuserheight map (b), a diffuser scatter PDF (c), and a diffuser (d) inaccordance with some embodiments.

DETAILED DESCRIPTION

Systems, methods, and media for recording an image using an opticaldiffuser are provided.

Turning to FIG. 1, an illustration of an image recording mechanism 102(e.g., a camera, video camera, mobile phone incorporating a camera,and/or any other suitable image recording mechanism) that is being usedto capture an image including three objects, A 104, B 106, and C 108, isshown. As can be seen, these objects are at different depths withrespect to mechanism 102. Because of limitations in the depth of fieldof mechanism 102, objects A 104 and C 108 may be out of focus whenmechanism 102 is focused on object B 106. For example, these objects maybe the toys shown in FIG. 2. As illustrated in FIG. 2(a), when a camerais focused on the center object (which may correspond to object B 106 ofFIG. 1), the other objects may be out of focus. By using the mechanismsas described herein, however, an image can be recorded of such objectsso that they appear to be in focus as illustrated in FIG. 2(b). This canbe referred to as mechanism 102 having an extended depth of field.

In accordance with some embodiments, extended depth of field can beachieved by incorporating a diffuser 110 or 112 into an image recordingmechanism 102. Recording an image using a diffuser in the pupil plane ofan image recording mechanism can be referred to as diffusion coding.Such a diffuser can be located at any suitable point in the imagerecording mechanism. For example, a diffuser 110 can be positionedbetween a light source (e.g., objects 104, 106, and 108) and a lens 114(e.g., as a lens attachment), a diffuser 112 can be positioned between alens 114 and a sensor 116 (e.g., as part of a lens or a camera body),etc.

The diffusion coding image can then be detected by sensor 116 and thenprovided to a hardware processor 118 (incorporated into mechanism 102)and/or a hardware processor 120 (external to mechanism 102) forsubsequent processing. This processing can include deblurring the sensedimage using a PSF that is matched to the PSF of the diffuser. Any othersuitable processing can additionally or alternatively be used. Aftersuch processing, an extended depth of field image can be presented on adisplay 124 (internal to mechanism 102) and/or a display 122 (externalto mechanism 102).

In order to illustrate how such an image can be recorded using adiffuser, the optics of some embodiments are now described.

As shown in FIG. 3, a light field L(ū,x) can be used to represent afour-dimensional set of rays propagating from an ideal lens witheffective focal length (EFL) f to a sensor. A vector ū=(u,v) can be usedto denote the coordinates on the u-v plane, which is coincident with theexit pupil of the lens, and a vector x=(x,y) can be used to denote thecoordinates on the x-y plane that is coincident with the sensor. Theirradiance E(x) observed on the sensor can be defined as the light fieldintegrated over all ray angles:

$\begin{matrix}{{{E\left( \overset{\_}{x} \right)} = {\int_{\Omega_{\overset{\_}{u}}}{{L\left( {\overset{\_}{u},\overset{\_}{x}} \right)}{\overset{\_}{u}}}}},} & (1)\end{matrix}$

where, Ω_(ū) is the domain of ū. For a scene with smooth depthvariation, locally, the captured image E(x) can be modeled as aconvolution between a depth-dependent PSF kernel P(x) and anall-in-focus image I(x).

As described further below, in accordance with some embodiments, acamera PSF can be shaped so that an image I(x) can be recovered from thecaptured image E(x) by deblurring with a single PSF P(x). Thedepth-dependence of the camera PSF can be analyzed by considering theimage produced by a unit energy point source. For example, as shown inFIG. 3, consider a point source whose image comes to focus at a distanced₀ from the aperture of the lens. Assuming a rectangular aperture ofwidth A, the light field produced by this point can be represented as:

$\begin{matrix}{{{L_{\delta}\left( {\overset{\_}{u},\overset{\_}{x}} \right)} = {\frac{1}{A^{2}} \sqcap {\left( \frac{\overset{\_}{u}}{A} \right){\delta \left( {\overset{\_}{x} - {s_{0}\overset{\_}{u}}} \right)}}}},} & (2)\end{matrix}$

where s₀=(d₀−f)/d is the defocus slope in light field space, and

is the box function:

$\begin{matrix}{{\sqcap \left( \frac{\overset{\_}{x}}{w} \right)} = \left\{ {\begin{matrix}1 & {{{{if}\mspace{14mu} {{\overset{\_}{x}}_{i}}} < \frac{1}{2}},\forall_{i}} \\0 & {otherwise}\end{matrix}.} \right.} & (3)\end{matrix}$

The image of this point is the camera PSF at the depth d₀, which is abox shaped PSF with defocus blur width s₀A:

$\begin{matrix}{{P(x)} = {\frac{1}{s_{0}^{2}A^{2}} \sqcap {\left( \frac{\overset{\_}{x}}{s_{0}A} \right).}}} & (4)\end{matrix}$

The effect of a general kernel D applied to a light field L, whichrepresents the effect of a diffuser placed in the aperture of a cameralens, can next be analyzed. The kernel can produce a new filtered lightfield {circumflex over (L)}, from which the modified PSF {circumflexover (P)} can be derived as:

$\begin{matrix}{{{\hat{L}\left( {\overset{\_}{u},\overset{\_}{x}} \right)} = {\int_{\Omega_{{\overset{\_}{u}}^{\prime}}}{\int_{\Omega_{{\overset{\_}{x}}^{\prime}}}{{D\left( {\overset{\_}{u},{\overset{\_}{u}}^{\prime},\overset{\_}{x},{\overset{\_}{x}}^{\prime}} \right)}{L\left( {{\overset{\_}{u}}^{\prime},{\overset{\_}{x}}^{\prime}} \right)}{{\overset{\_}{u}}^{\prime}}{{\overset{\_}{x}}^{\prime}}}}}},} & (5) \\{{{\hat{P}\left( \overset{\_}{x} \right)} = {\int_{\Omega_{u}}{{\hat{L}\left( {\overset{\_}{u},\overset{\_}{x}} \right)}{\overset{\_}{u}}}}},} & (6)\end{matrix}$

where Ω_({circumflex over (x)}) is the domain of x. This approach allowsa large class of operations applied to a light field to be expressed.For instance, consider a kernel of the form

$\begin{matrix}{{D\left( {\overset{\_}{u},{\overset{\_}{u}}^{\prime},\overset{\_}{x},{\overset{\_}{x}}^{\prime}} \right)} = {{\frac{1}{w^{2}}{\delta \left( {\overset{\_}{u} - {\overset{\_}{u}}^{\prime}} \right)}} \sqcap {\left( \frac{\overset{\_}{x} - {\overset{\_}{x}}^{\prime}}{w} \right).}}} & (7)\end{matrix}$

Note that here D takes the form of a separable convolution kernel withfinite support in the x domain. The geometric meaning of this kernel canbe illustrated as shown in FIG. 4. As shown, each ray in the light fieldis blurred so that, instead of piercing the sensor at a single location,it contributes to a square of width w. In order to understand the effectof the diffuser, an image E captured without the diffuser can becompared to an image Ê captured with it. For this diffuser kernel,substituting Equation 7 into Equations 5 and 6 gives:

$\begin{matrix}{{{\hat{P}\left( \overset{\_}{x} \right)} = {\frac{1}{w^{2}} \sqcap {\left( \frac{\overset{\_}{x}}{w} \right) \otimes {P\left( \overset{\_}{x} \right)}}}},} & (8)\end{matrix}$

where {circle around (×)} denotes convolution. The modified PSF can bethe camera PSF blurred with a box function. Therefore, the effect of thediffuser is to blur the image that would be captured were it notpresent. However, the diffuser given by the kernel in Equation 7 may notbe useful for extending depth of field because it does not increasedepth independence or preserve high frequencies in the camera PSF.

In general, the kernel for any diffuser that is placed in the aperturecan be represented as:

D(ū,ū′,x,x ′)=δ(ū−ū′)k(ū,x−x ′),  (9)

where k is called the scatter function. As can be seen, the diffuser hasno effect in the ū domain, but has the effect of a convolution in the xdomain. For the diffuser given by Equation 7, the scatter function canbe represented as a two-dimensional box function:

${k\left( {\overset{\_}{u},\overset{\_}{x}} \right)} = {\frac{1}{w^{2}} \sqcap {\left( \frac{\overset{\_}{x}}{w} \right).}}$

By changing from rectangular coordinates (u,v,x,y) to polar coordinates(ρ,φ,r,θ) using the relations u=ρ cos φ, v=ρ sin φ, x=r cos θ, and y=rsin θ, a polar system where ρ,rε(—∞,∞) and θ,φε(0,π) and a circularaperture with diameter A can be considered. In this system, the lightfield representing a unit-energy point source located at distance d₀ canbe written as:

$\begin{matrix}{{{L_{\delta}\left( {\rho,r} \right)} = {\frac{4}{\pi \; A^{2}} \sqcap {\left( \frac{\rho}{A} \right)\frac{\delta \left( {r - {s_{0}\rho}} \right)}{\pi {r}}}}},} & (10)\end{matrix}$

which is independent of both θ and φ because the source is isotropic.Note that verifying unit-energy can be carried out trivially byintegrating L_(δ)(ρ,r) in polar coordinates. Comparing theparameterizations for the light field of a point source in Equations 2and 10, it can be seen than a slice of L_(δ)(x,y) represents a singleray, while a slice L(ρ,r) represents a 2D set of rays. In the radiallysymmetric parameterization, a slice of the light field represents aconic surface connecting a circle with radius ρ in the aperture plane toa circle of radius r on the sensor (see FIG. 5).

A radially symmetric diffuser produces a drastically different effectthan the diffuser given by Equation 7. When a radially symmetricdiffuser is introduced, neither the diffuser nor the lens deflects raystangentially, and therefore the diffuser kernel and modified light fieldcan be represented using the reduced coordinates (ρ,r). Equations 5 and6 then become:

$\begin{matrix}{{{\hat{L}\left( {\rho,r} \right)} = {\pi^{2}{\int_{\Omega_{\rho}}{\int_{\Omega_{r}}{{D\left( {\rho,\rho^{\prime},r,r^{\prime}} \right)}{L\left( {\rho^{\prime},r} \right)}{\rho^{\prime}}{\rho^{\prime}}{r^{\prime}}{r^{\prime}}}}}}},} & (11) \\{{{E(r)} = {\pi {\int_{\Omega_{\rho}}{{\hat{L}\left( {\rho,r} \right)}{\rho }{\rho}}}}},} & (12)\end{matrix}$

and the general form of the diffuser kernel becomes:

$\begin{matrix}{{D\left( {\rho,\rho^{\prime},r,r^{\prime}} \right)} = {\frac{\delta \left( {\rho - \rho^{\prime}} \right)}{\pi {\rho^{\prime}}}\frac{k\left( {{r - r^{\prime}},\rho} \right)}{\pi {r}}}} & (13)\end{matrix}$

The same box-shaped scattering function as was used for the diffuserkernel in Equation 7 can be used for Equation 13:

$\begin{matrix}{{k\left( {r,\rho} \right)} = {\frac{1}{w} \sqcap {\left( \frac{r}{w} \right).}}} & (14)\end{matrix}$

However, the physical interpretation of this diffuser is different thanthe previous diffuser. For the previous diffuser, each ray in the lightfield is scattered so that it spreads across a square on the sensor. Theeffect of the scattering function in Equation 14, however, is asillustrated in FIG. 6. As shown, in the absence of the diffuser, lightfrom an annulus of width dρ and radius ρ in the aperture plane projectsto an annulus of width dr and radius r on the sensor. The effect of thescatter function in Equation 14 is to spread the light incident on thesensor so that it produces an annulus of width w instead.

As illustrated by volume 602 in FIG. 6, in polar coordinates, a ray canbe a small annular section that travels from the aperture plane to thesensor plane. The effect of the diffuser, which is to scatter a rayalong a radial line of width w, can be as illustrated by volume 604.

A box-shaped scatter function can be used here for notationalconvenience, but a Gaussian scattering function (e.g., as illustrated inFIG. 9(c)) can be superior for extended DOF imaging. The light field ofa point source filtered by this diffuser kernel and PSF can be shown tobe:

$\begin{matrix}{{{\hat{L}\left( {\rho,r} \right)} = {\frac{4}{\pi \; A^{2}} \sqcap {\left( \frac{\rho}{A} \right)\frac{\sqcap \left( \frac{r - {s_{0}\rho}}{w} \right)}{\pi \; w{r}}}}},} & (15) \\{{\hat{P}(r)} = {\frac{4}{\pi \; s_{0}^{2}A^{2}}{{\frac{1}{w{r}}\left\lbrack {\sqcap {\left( \frac{r}{w} \right) \otimes \left( {\sqcap {\left( \frac{r}{s_{0}A} \right) \cdot {r}}} \right)}} \right\rbrack}.}}} & (16)\end{matrix}$

The analytic solution for this PSF is a piecewise function due to thecontribution from the term in brackets, which is a convolution betweenthe two rect functions (one weighted by |r|). Note that as thescattering width w is reduced to zero, the first rect (combined with1/w) approaches a delta function and the result is a pillbox-shapeddefocus PSF. Also note that if a different diffuser with differentscattering function is used, the first rect is simply replaced with thenew scattering function. However, the convolution term is far lesssignificant than the 1/|r| term, whose effect dominates, resulting in aPSF which can be strongly depth independent while still maintaining astrong peak and preserving high frequencies.

As illustrated in FIG. 6, light incident on a small annular region ofwidth δr and radius r emanates from an annulus in the aperture, and itsenergy can be proportional to ρ or equivalently to r/s₀. This explainsthe presence of the |r| multiplier within the term in brackets ofEquation 16. This term in brackets states that the energy in a pillboxdefocus PSF annulus is spread uniformly along radial lines of width w bythe diffuser, as shown on the right hand side of FIG. 6. The 1/|r| termin Equation 16 can be attributed to the fact that the energy densitybecomes larger for light that is scattered closer to the center of thePSF.

FIG. 7 shows several PSF 702 and Modulation Transfer Function (MTF) 704graph pairs for a camera with (714, 716, 718, 720, 722, 724, 726, and728) and without (715, 717, 719, 721, 723, 725, 727, and 729) thediffuser given by Equation 16. The defocus blur diameter s₀A changesbetween 0 pixels 706, 25 pixels 708, 50 pixels 710, and 100 pixels 712.The scatter function of Equation 14 is a Gaussian instead of a boxfunction, and the diffuser parameter w (the variance of the Gaussian) ischosen so that w=100 pixels. Note that when the diffuser is present,there is little variation with depth for either the PSF or MTF.Introducing the diffuser also eliminates the zero crossings in the MTF.For smaller defocus values, the diffuser suppresses high frequencies inthe MTF. However, because the diffuser MTF does not vary significantlywith depth, high frequencies can be recovered via deconvolution.

In accordance with some embodiments, diffusers of the “kinoform” type(as described in Caufield, H. J., “Kinoform Diffusers,” In SPIEConference Series, vol. 25, p. 111, 1971, which is hereby incorporatedby reference herein in its entirety) where the scattering effect iscaused entirely by roughness variations across a surface can be used.Such a diffuser can be considered to be a random phase screen, andaccording to statistical optics, for a camera with effective focallength f, and center wavelength X, the effect of placing this screen inthe aperture of the camera can result in the following:

$\begin{matrix}{{{\hat{P}\left( {x,y} \right)} \propto {p_{\varphi_{u},\varphi_{v}}\left( {\frac{x}{\overset{\_}{\lambda}\; k},\frac{y}{\overset{\_}{\lambda}\; k}} \right)}},} & (18)\end{matrix}$

where φ_(u) and φ_(v) are the u and v derivatives of the phase shiftinduced by the surface, and p_(φ) _(x) _(,φ) _(y) is the jointprobability of these derivatives. The result of Equation 18 is that adiffuser can be implemented by creating an optical element withthickness t(u,v), where the gradient of this surface ∇t(u,v) is sampledfrom a probability distribution which is also a desired PSF.Intuitively, this equation can be understood as follows: p_(φ) _(u)_(,φ) _(v) denotes the fraction of the surface t(u,v) with slope(φ_(u),φ_(v)). For small angles, all incoming rays incident on thisfraction of the surface will be deflected at the same angle, since theslope is constant over this region. Thus, the quantity p_(φ) _(u) _(,φ)_(v) also reflects the portion of light that will be deflected by theslope (φ_(x),φ_(y)).

A Kinoform diffuser has a randomly varying surface with a generalprobability distribution of slopes as illustrated in FIG. 8(b). Kinoformdiffusers can be thought of as generalized phase plates. For example, aregular deterministic phase plate with thickness t(u)=aλu, as shown inFIG. 8(a), can also be thought of as having a slope drawn from aprobability function p(φ_(u)) which is a delta function. The result ofplacing this phase plate in the pupil plane of a camera is to shift thePSF, which can be thought of as convolving p(φ_(u)) with the PSF.

To implement the diffuser defined in Equation 14, the diffuser surfacecan be implemented as a sequence of quadratic elements whose diameterand sag is drawn from a random distribution as described in Sales, T. R.M., “Structured microlens arrays for beam shaping,” Optical Engineering42, 11, pp. 3084-3085, 2003, which is hereby incorporated by referenceherein in its entirety. The scatter function of the diffuser can bedesigned to be roughly Gaussian with 0.5 mm variance (corresponding tow=1 mm in Equation 16) as shown in FIG. 9(c). To create a radiallysymmetric diffuser, a one-dimensional random profile can be created andthen a polar transformation applied to create a two-dimensional surface(see, e.g., FIGS. 9(a) and 9(b)).

In some embodiments, a diffuser can be made using laser etching.

In some embodiments, the maximum height of the diffuser surface can be 3μm, and the diffuser can be fabricated using a laser machiningtechnology which has a minimum spot size of about 10 μm. To ensure thateach quadratic element in the diffuser is fabricated with high accuracy,the minimum diameter of a single element can be chosen to be 200 μm,resulting in a diffuser with 42 different annular sections.

Any suitable hardware can be used to implement a mechanism 102 inaccordance with some embodiments. For example, a Canon EOS 450D sensorfrom Canon U.S.A., Inc. can be used as sensor 116, a 22 mm diameterdiffuser (e.g., as illustrated in FIG. 9(d)) that is laser etched in apiece of suitable optical glass by RPC Photonics of Rochester, N.Y. canbe used as diffuser 110 or 112, and a 50 mm f/1.8 lens from CanonU.S.A., Inc. can be used as lens 114. As another example, lens 114 canhave any focal length and consist of refractive optics, reflectiveoptics, or both. For instance, a 3048 mm focal length Meade LX200telescope (available from) can be used in some embodiments.

In accordance with some embodiments, any suitable processing can beperformed to deblur the image hitting a camera sensor after passingthrough a lens and diffuser (in either order). For example, the Wienerdeconvolution with the PSF at the center depth can be used to deblur thesensed images. Any suitable additional or alternative processing on theimages can be used. For example, additional deblurring of diffusioncoded images can performed using the BM3D deblurring algorithm asdescribed in Dabov, K., Foi, A., Katkovnik, V., and Egiazarian, K.,“Image restoration by sparse 3D transform-domain collaborativefiltering,” In SPIE Conference Series, vol. 6812, 681207, 2008, which ishereby incorporated by reference herein in its entirety. In someembodiments, the BM3D deblurring algorithm enforces a piecewisesmoothness prior that suppresses the noise amplified by the deblurringprocess.

Any suitable hardware processor, such as a microprocessor, digitalsignal processor, special purpose computer (which can include amicroprocessor, digital signal processor, a controller, etc., memory,communication interfaces, display controllers, input devices, etc.),general purpose computer suitably programmed (which can include amicroprocessor, digital signal processor, a controller, etc., memory,communication interfaces, display controllers, input devices, etc.),server, programmable gate array, etc. can be used to deblur the imagecaptured by the sensor. Any suitable hardware can by used to transferthe image from the sensor to the processor. Any suitable display,storage device, or printer can then be used to display, store, or printthe deblurred image.

In some embodiments, any suitable computer readable media can be usedfor storing instructions for performing the processes described herein.For example, in some embodiments, computer readable media can betransitory or non-transitory. For example, non-transitory computerreadable media can include media such as magnetic media (such as harddisks, floppy disks, etc.), optical media (such as compact discs,digital video discs, Blu-ray discs, etc.), semiconductor media (such asflash memory, electrically programmable read only memory (EPROM),electrically erasable programmable read only memory (EEPROM), etc.), anysuitable media that is not fleeting or devoid of any semblance ofpermanence during transmission, and/or any suitable tangible media. Asanother example, transitory computer readable media can include signalson networks, in wires, conductors, optical fibers, circuits, anysuitable media that is fleeting and devoid of any semblance ofpermanence during transmission, and/or any suitable intangible media.

Although the invention has been described and illustrated in theforegoing illustrative embodiments, it is understood that the presentdisclosure has been made only by way of example, and that numerouschanges in the details of implementation of the invention can be madewithout departing from the spirit and scope of the invention, which isonly limited by the claims which follow. Features of the disclosedembodiments can be combined and rearranged in various ways.

What is claimed is:
 1. A system for recording an image of a scene,comprising: a diffuser that behaves in accordance with a scatteringfunction so that light representing the scene entering a first side ofthe diffuser is output by a second side of the diffuser as a blurredform of the light representing the scene; an image sensor that receivesthe blurred form of the light representing the scene and generates imagedata representing a first image based on the blurred form of the lightrepresenting the scene; and a hardware processor that uses a pointspread function corresponding to the scattering function to generate asecond image based on the image data representing the first image andthat corresponds to a deblurred version of the first image.
 2. Thesystem of claim 1, wherein the diffuser is radially symmetric.
 3. Thesystem of claim 1, wherein a one-dimensional thickness profile of theradially symmetric diffuser along a radial direction is random.
 4. Thesystem of claim 3, wherein the diffuser is a kinoform type diffuser. 5.The system of claim 1, wherein the scattering function is a symmetricdistribution function.
 6. The system of claim 1, wherein the systemcomprises a camera having an aperture, and wherein the scatteringfunction does not vary as a function of aperture coordinates ofdescribing the aperture.
 7. The system of claim 1, further comprising alens through which the light representing the scene passes before it isincident on the first side of the diffuser.
 8. The system of claim 1,further comprising a lens through which the blurred form of the lightrepresenting the scene passes before it is incident on the image sensor.9. The system of claim 1, further comprising a display that displays thedeblurred image.
 10. A method for recording an image of a scene,comprising: diffusing light representing the scene using a diffuser thatbehaves in accordance with a scattering function so that the lightrepresenting the scene entering a first side of the diffuser is outputby a second side of the diffuser as a blurred form of the lightrepresenting the scene; receiving the blurred form of the lightrepresenting the scene using an image sensor; generating image datarepresenting a first image based on the blurred form of the lightrepresenting the scene received by the image sensor; and generating asecond image that corresponds to a deblurred version of the first imagebased on the image data representing the first image using a pointspread function corresponding to the scattering function.
 11. The methodof claim 10, wherein the diffuser is radially symmetric.
 12. The methodof claim 10, wherein a one-dimensional thickness profile of the radiallysymmetric diffuser along a radial direction is random.
 13. The method ofclaim 12, wherein the diffuser is a kinoform type diffuser.
 14. Themethod of claim 10, wherein the scattering function is a symmetricdistribution function.
 15. The method of claim 10, further comprisingpassing the light representing the scene through a camera aperturebefore it is incident on the first side of the diffuser, wherein thescattering function does not vary as a function of aperture coordinatesof describing the aperture.
 16. The method of claim 10, furthercomprising passing the light representing the scene through a lensbefore it is incident on the first side of the diffuser.
 17. The methodof claim 10, further comprising passing the blurred form of the lightrepresenting the scene through a lens before it is incident on the imagesensor.
 18. The method of claim 10, further comprising displaying thedeblurred image using a display.